Ionosphere delay measurement using carrier phase

ABSTRACT

One or more atmospheric propagation effects are estimated by using a phase comparison between and upper sideband and a lower sideband of a modulated signal. In one embodiment, one or more propagation effects are estimated by using a phase comparison between an upper sideband and a lower sideband of a satellite navigation signal. In one embodiment, one or more ionospheric propagation effects are estimated by using a phase comparison between an upper sideband and a lower sideband of a GPS M-code signal.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a divisional application of U.S. application Ser.No. 11/127,772, filed May 12, 2005 now U.S. Pat. No. 7,375,680, theentirety of which is incorporated by reference herein.

BACKGROUND

1. Field of the Invention

The present invention relates to measurement of ionospheric propagationeffects on Radio Frequency (RF) signals by comparing carrier phasebetween signals of different frequency, such as, for example, upper andlower sidebands of a GPS M-code signal.

2. Description of the Related Art

In the upper regions of the earth's atmosphere, ultraviolet and X-rayradiation coming from the sun interact with the atmospheric gasmolecules and atoms. These interactions result in ionization giving riseto large numbers of free “negatively charged” electrons and “positivelycharged” atoms and molecules. The region of the atmosphere where gasionization takes place is called the ionosphere. It extends from analtitude of approximately 50 km to about 1,000 km or higher (the upperlimit of the ionospheric region is not clearly defined).

The electron density within the ionosphere is not constant. It changeswith time and altitude. The ionospheric region is typically divided intosub-regions, or layers, according to the electron density. These layersare named D (50-90 km), B (90-140 km), F1 (140-210 km), and F2(210-1,000 km), respectively, with F2 usually being the layer of maximumelectron density. The altitude and thickness of these layers vary withtime, as a result of the changes in the sun's radiation and the earth'smagnetic field. For example, the F1 layer largely disappears during thenight and is more pronounced in the summer than in the winter.

The ionosphere is a dispersive medium, which means that RF waves withthe same origination point, but different frequencies, will travel atdifferent speeds and along different ray paths as they pass through thevarious ionospheric layers. In the case of satellite navigation systems,such as, for example, the Global Positioning System (GPS), bending ofthe signal propagation path causes a relatively small range error,particularly if the satellite elevation angle is greater than 50degrees. However, the change in the propagation speed causes asignificant range error, and therefore should be accounted for. Theionosphere speeds up the phase velocity of the RF wave. The ionospherealso slows down the group velocity. The code frequency is thefundamental parameter used to determine the space vehicle (SV) rangefrom the receiver while the carrier frequency is primarily used tomaintain tracking of the SV signal and to help determine vehiclemovement.

The ionospheric delay is proportional to the number of free electrons,called the Total Electron Content (TEC), along the signal path. TEC,however, depends on a number of factors, such as: the time of day; thetime of year; the 11-year solar cycle; and the geographic location(electron density levels are minimum in mid-latitude regions and highlyirregular in polar, auroral, and equatorial regions). As the ionosphereis a dispersive medium, it causes a delay that is frequency dependent.The delay is greater for lower frequencies than for higher frequencies.Thus, for GPS signals, the ionospheric delay is greater at the L2carrier frequency than that of the L1 carrier frequency. Generally,ionospheric delay is of the order of 0.5 meters to 15 meters, but canreach over 150 meters under extreme solar activities, at midday, andnear the horizon.

Taking advantage of the ionosphere's dispersive nature, the ionosphericdelay can be determined with a relatively high degree of accuracy bymeasuring the “time of flight” between two RF signals of differentfrequencies that travel along similar paths. In GPS this dual frequencymeasurements may be accomplished by comparing the P(Y)-code pseudorangemeasurements between the L1 and L2 frequency bands.

Single frequency band receivers cannot take advantage of the dispersivenature of the ionosphere. They can, however, use an empiricalionospheric model to correct some portion of the error introduced bydispersion. The most widely used model is the Klobuchar model, whosecoefficients are transmitted as part of the navigation message. Anothersolution for users with single-frequency GPS receivers is to usecorrections from regional networks. Such corrections can be received inreal time through other communication links.

SUMMARY

These and other problems are solved by a system wherein one or morepropagation effects are estimated by using a phase comparison betweenand upper sideband and a lower sideband of a multi-carrier modulatedsignal including, but not limited to, binary offset carrier signals. Inone embodiment, one or more propagation effects of a dispersive mediumare estimated by using a phase comparison between an upper sideband anda lower sideband of a GPS M-code signal. In one embodiment, one or moreionospheric propagation effects are estimated.

In one embodiment, hardware and software for ionospheric measurementsare based on a single-band of a receiver by comparing the phase of upperand lower modulation sidebands. In one embodiment, a receiver providesimproved quality, redundancy, resistance to spoofing, and/or resistanceto jamming by making separate ionospheric measurements by comparingupper and lower modulation sidebands from signals transmitted usingcarriers in different frequency bands. In one embodiment, a GPS receiverprovides ionospheric measurements by comparing the phase relationshipbetween an upper modulation sideband and a lower modulation sideband ofthe L1 signal, and by separately comparing an upper modulation sidebandand a lower modulation sideband of the L2 signal. This provides tworelatively independent measurements for each satellite.

In one embodiment, ionospheric measurement obtained by comparing thephase of an upper modulation sideband and a lower modulation sideband isused, at least in part, to verify that a received signal was generatedfrom a desired source (e.g., from space vehicle or artificial satellite)and not from an undesired source (e.g., a spoofer). A potential spoofercan be detected, because each satellite has an expected USB/LSB phaseshift in the L1 and/or L2 M-code signals based on the satellitesaltitude above the horizon and the expected ionospheric properties.

In one embodiment, relative phase measurement obtained by comparing thephase of an upper modulation sideband and a lower modulation sideband,is used to assist in resolving the phase ambiguity.

In one embodiment, a phase relationship between an upper modulationsideband and a lower modulation sideband, is modulated to encode a datasignal into the phase relationship.

In one embodiment, a measurement of a phase relationship between anupper modulation sideband and a lower modulation sideband, is used toevaluate phase tracking performance, relative to offset carrier signaltracking, in the presence of ionospheric distortion.

In one embodiment, ionospheric measurement obtained by comparing thephase of an upper modulation sideband and a lower modulation sideband isused to monitor relatively short-term ionospheric TEC levels and/orionospheric TEC levels of single events, such as, for example,scintillations of the ionosphere. Natural or man-made scintillationevents can be monitored.

In one embodiment, a communication system includes controlling the TECbetween a signal generator and receiver such that the resulting changein phase between an upper modulation sideband and a lower modulationsideband can be decoded to obtain a data message.

In one embodiment, a measurement obtained by comparing the phase of anupper modulation sideband and a lower modulation sideband of a modulatedsignal is used to correct the phase between the upper modulationsideband such that the signal can be demodulated to recover themodulation data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows propagation from a satellite to a ground-based or airbornereceiver with ionospheric propagation.

FIG. 2 shows sample spectra of the GPS L1 and L2 M-code signals.

FIG. 3 shows obliqueness as a function of relative elevation anglebetween the satellite and the receiver.

FIG. 4 shows an example of the relative phase angle of L1 and L2 as afunction of total electron count.

FIG. 5 shows calculated Total Electron Count (TEC) values using relativephase angles determined from actual TEC values.

FIG. 6 is a block diagram of a satellite navigation receiver configuredto estimate ionospheric parameters from lower and upper sidebandcomponents of a satellite signal.

FIG. 7 consists of FIGS. 7A and 7B and is a signal processing blockdiagram of a GPS receiver configured to provide ionospheric carrierphase correction.

DETAILED DESCRIPTION

FIG. 1 shows propagation of signals from a satellite 101 along apropagation path 103 to a receiver 102. A portion of the propagationpath 103 passes through the ionosphere 105.

The ionosphere 105 is a dispersive medium, which means the path taken bythe radio frequency signal is frequency dependent. Additionally, thespeed at which the radio frequency travels through the ionosphere isalso frequency dependent. As a result of these effects, the radiofrequency bends along the trajectory from the satellite 101 and changesits group and wave velocity as the radio frequency signals propagatealong the path 103 through the ionospheric layers to reach the receiver102. In the case of satellite navigation systems, such as, for example,the Global Positioning System (GPS), bending of the signal propagationpath 103 causes a relatively small range error, particularly if thesatellite 101 elevation angle φ is sufficiently large. However, thechange in the propagation speed causes a measurable range error. Thisrange error is typically the largest source of error when calculatingnavigation solutions. The ionosphere 105 increases the phase velocitybeyond the speed of light, while it reduces the group velocity. That is,the apparent distance along the path 103 will be too long if measured bythe code data. The velocity changes in the radio frequency signal giverise to a pseudorange error.

The ionosphere 105 is a dispersive medium, and it causes a delay that isfrequency dependent. The delay is greater for lower frequencies than forhigher frequencies. Thus, for GPS signals, the L2 ionospheric delay isgreater than that of L1.

Currently, two fundamental methods are used to calculate the group delayassociated with the ionosphere 105. The first requires a singlefrequency band, an ionospheric model, and coefficients for that modelsupplied in the GPS data message. The other method uses the codeinformation sent on the L1 frequency band, which is compared with thecode information generated in the receiver to measure the time of flightfor that signal. Then a similar code measurement is made using the codeinformation from the L2 frequency band. The difference in time of flightbetween these two frequency band code signals is used to compute thetotal number of electrons encountered by the radio frequency wave as ittraveled along its path. This difference in time of arrival between thetwo separate code signals from different bands is used to compensate forthe atmospheric effects in the ionosphere 105. Both of these methodshave advantages and disadvantages.

The single frequency band model has the simplicity of design of onlyneeding to track one code signal. However, the accuracy of theionosphere 105 model, is such that the model will provide at least a 50percent reduction in the single frequency user's root mean square (RMS)position error due to ionospheric propagation effects. Additionally, theunspecified periodicity of the model coefficients typically make theionosphere range error to be less than 25% the true value. This is aconcern because, uncorrected atmosphere delays can range from 2.4 m to5.2 m if the angle of elevation between the satellite 101 and receiver102 is known. In extreme cases this error can increase by as much as 30m. This atmospheric error is larger than other errors by almost a factorof two. If the angle of elevation is not known, then due to theobliqueness of the satellite 101, the error could further increase by asmuch as a factor of three. These range errors are acceptable for somesituations but for others a more precise method of accounting for theionosphere 105 needs to be implemented.

The dual frequency band ionosphere 105 correction method has asignificantly higher level of precision than its single frequency bandcounterpart. This method uses the relative time of arrival delay betweenthe L1 and L2 frequency bands launched at the same place and time. Thistime differential is used to calculate the Total Electron Content TECfor the ionosphere correction used in GPS measurements. This TEC numberis then used for ionospheric time delay corrections. These timecorrections are then used to help convert the pseudorange to the truedistance between the satellite 101 and the receiver 102. The accuracy ofthis method depends on the noise of the system. The error introduced bythis noise is on the order of ˜1 m. The time delay between twofrequencies (f₁ f₂) as a function of TEC is given by:

$\begin{matrix}{{\Delta\; t} = {\frac{TEC}{c \cdot}(40.3081926)\left( {\frac{1}{f_{2}^{2}} - \frac{1}{f_{1}^{2}}} \right)}} & (1)\end{matrix}$

The time delay as a function of TEC for the GPS L1 and L2 signals is:

$\begin{matrix}{t_{delay} = \frac{{TEC} \cdot 40.3081926}{{cf}^{2}}} & (2)\end{matrix}$

A beneficial feature of this method is the relatively large frequencyspread between the L1 and L2 frequencies. This difference is useful inmitigating the error caused by the relative code measurement algorithms.The downside to this method is the requirement that two modulatedcarriers be tracked and processed. These additions result in greaterhardware and software requirements than a single-band method.

The spectrum of a typical offset carrier modulated signal, shown in FIG.2, has two sub-carrier modulation sideband lobes, shown as a LowerSideBand (LSB) 201 centered at F_(L), and an Upper SideBand (USB) 202centered at F_(U). For example, in a GPS system the M-code signal ismodulated onto both the L1 and the L2 carriers, thus providing twosub-carrier modulation sidebands with center frequencies F_(U) and F_(L)for each of the L1 and L2 bands. For the L1 signal, the centerfrequencies F_(U) and F_(L) of the LSB 201 and the USB 202 areapproximately 153*10.23 MHz and 155*10.23 MHz respectively. For the L2signal, the LSB and USB center frequencies F_(U) and F_(L) areapproximately 119*10.23 MHz and 121*10.23 MHz, respectively. For eitherL1 and/or L2 tracking, both sidebands of the signal are coherentlyaffected by the difference in ionospheric delay between the upper andlower sidebands.

The ionospheric delay is approximately inversely proportional to thecarrier frequency squared. The ionospheric delay at L1 (1575.42 MHz),expressed in distance traveled, can fluctuate from 0.5 meter to 60meters or more. Calculation of the difference in propagation delaybetween upper and lower sideband center frequencies gives pseudorangedifferences as small as 0.025 meters and at least as large as 1.6meters. Translated to carrier cycles at USB or LSB frequencies, theangular displacement can range from 0.07 cycles to 8.3 cycles. When theUSB and the LSB have an angular displacement of one half cycle, the USBand LSB tend to be approximately 180 degrees of phase.

The center frequencies of the LSB 201 and the USB 202 are closertogether than the L1 and L2 center frequencies. Nevertheless, in oneembodiment, tracking the carrier phase difference between the USB andthe LSB yields ionospheric delay estimates of higher quality than thoseobtained by differencing the pseudorange measurements from L1 and L2because carrier tracking is more accurate than code tracking. Thus, theionospheric delay difference can be estimated with much smallermeasurement error in the receiver 102.

The speed of a wave as it travels through the ionosphere 105 depends onthe density of the plasma along the path 103 of the satellite signal.This density is commonly referred to as the total number of electrons ina square meter that the wave encounters along the path 103 between thesatellite 101 and the receiver 102. This leads to a relationship shownin Equation (1) between the time the signal is launched from thesatellite 101 to the time the signal is received. This total time delaycan then be related to the phase of the frequency by the relationship:

$\begin{matrix}{\theta_{i} = {{t_{delay}f_{i}360} = \frac{{TEC} \cdot 4.8403317 \cdot 10^{- 5}}{f_{i}}}} & (3)\end{matrix}$

This phase delay is the total phase delay associated with thatfrequency. Additionally, Equation (1) shows that as the TEC increasesthe phase delay observed will also increase. Unfortunately, most systemscan only measure the remainder of the total phase delay resulting in avalue between −180° and 180°. This limitation results in lostinformation regarding the number of cycles the wave has undergone whiletraveling from the satellite 101 to the receiver 102. Eventually theobserved phase angle will increase beyond 360° and the phase angle willbe indistinguishable between TEC values with similar phase angles(integer ambiguity). The amount of TECu change before a phase anglerepeats is called the TEC range. TECu is the total electron count unit,which is 10¹⁶el/m².

TEC values that occur naturally and at maximum obliqueness angle canvary from 1 TECu to 300 TECu. Significant parameters that impact the TECencountered by the GPS signals include the time of day (TOD) and angleof elevation φ of the satellite 101. As an example, to calculate the TECas a function of time, the TOD historical data taken during a period ofthe Earth's greatest sunspot activity demonstrates that over the courseof an hour, the mean maximum rate of increase is 0.004×10¹⁶ el/m²s. Atthe extreme, the upper limit to the rate of change of TEC isapproximately 0.1×10¹⁶ el/m²s. However, it is unlikely that this ratewould continue beyond a few minutes. The second factor that affects theTEC in the ionosphere 105 is the angle φ of the satellite 101 inreference to the receiver 102. This factor is called the obliqueness Qgiven by:

$\begin{matrix}{{Q(\varphi)} = \left( {1 - \left( \frac{R_{e}{{Sin}(\varphi)}}{R_{S}} \right)^{2}} \right)^{- \frac{1}{2}}} & (4)\end{matrix}$

-   -   where R_(E) is the Radius of the Earth and R_(S) is the distance        from center of the earth to the satellite 101.

The factor Q is a nonlinear function that depends on the angle ofelevation between the satellite 101 and the receiver 102. At φ=90°, Q=1and at φ=5°, Q=˜3. By virtue of φ, the TEC can increase significantly,and consequently the Q factor reduces a TECu range for a given frequencyband by its inverse (1/Q).

Equation (5) models how the TEC levels changes over a 24 hour period (T)and angle of elevation assuming the TEC follows a sinusoidal patternduring the course of the day. This model also assumes a minimum TECvalue 0 TECu with the maximum value of ˜100 TECu. While a more detailedmodel similar to the one used for single frequency GPS measurementscould be used, it is typically not necessary.

$\begin{matrix}{{{TEC}\left( {Q,t} \right)} \approx {Q \cdot \left\lbrack {{50\;{\sin\left( \frac{2\;{\pi \cdot t}}{T} \right)}} + 50} \right\rbrack}} & (5)\end{matrix}$

Using Equation (5), the required TEC range to unambiguously calculatethe TEC, and thus correct for the ionospheric delays, the combination ofQ and t consideration is given by Equation (6), where TEC_(max) is themaximum amount of TEC to be found in the ionosphere 105 (nominally 100TECu) is:

$\begin{matrix}{{{TEC}_{Range}\left( {Q,t} \right)} \geq {Q \cdot \frac{2 \cdot {TEC}_{\max} \cdot t}{T}}} & (6)\end{matrix}$

Typically, TEC_(max)=100, Q={1:3}, and t={12 hr-1 hr}. The extra factorof 2 in the sine term is due to the range of allowable time before theTEC calculation could be incorrect. The range of Q is from 1-3 and therange of t is 12h-1h. The Q factor is a function of the satellite 101location and cannot be controlled by the receiver 102. However, if the Qis known then it is possible to use that information to eliminateunrealistic TEC values. The 1 hour minimum is due to the uncertainty ofthe ionosphere 105 model based on historic data and possiblefluctuations. These equations illustrate that the more well known the φis, then the less the time of day needs to be known and vise versa.Equation (6) is useful because it gives the required TEC range touniquely determine the TEC by using input parameters. The TECu range canbe centered on the most probable TEC value and implement the carrierphase information to uniquely determine the TEC. With aproperly-determined TEC an ionosphere 105 correction can be made.

To determine which carrier phase to measure when calculating the TEC ofthe ionosphere 105 are two competing factors to be considered. Thesefactors can be seen in Equation (7), which gives the phase change as afunction of frequency and TEC.

$\begin{matrix}{{\theta\left( {f,{TEC}} \right)} = {\frac{TEC}{c \cdot f} \cdot 360^{\circ} \cdot 40.308}} & (7)\end{matrix}$

-   -   where c=299792458 m/s.

As the frequency of a signal increases, the resolution in determiningthe delay of the signal increases. However, as the frequency increases,the TEC range of the signal is lowered. Table 1 lists the TEC range ofM-Code frequencies and the TECu change to cause a 10° phase anglechange. Therefore, the ideal signal wavelength to be implemented is abalance of these two factors as dictated by the users needs. Possiblecandidates for phase measurements are the carrier frequencies of the L1USB, L1 LSB, L2 USB, L2 LSB or a combination of these frequencies.

TABLE 1 Signal Description Frequency TEC Range TECu/1° L1 USB 1585.65MHz 1.18 TECu 0.0033 L1 LSB 1565.19 MHz 1.16 TECu 0.0032 L2 USB 1237.83MHz 0.92 TECu 0.0026 L2 LSB 1217.37 MHz 0.91 TECu 0.0025

The phase angles of the individual frequencies are difficult to measureand increase too rapidly to be useful for TEC measurements requiring anysignificant TEC range.

TABLE 2 FREQUENCY Wavelength Range Error (±15°)   10.23 MHz (Code data)  ~29 m ~0.5 m Time Delay Error (1.67 ns) 1217.37 MHz (L2 LSB) ~0.25 m ~0.01 m 1237.83 MHz (L2 USB) ~0.25 m  ~0.01 m 1564.19 MHz (L1 LSB)~0.19 m ~0.008 m 1585.65 MHz (L1 USB) ~0.19 m ~0.008 m

One measurement that can consistently be made is the relative carrierphase angle (θ_(rel)) between the upper side band (USB) and the lowersideband (LSB) of the L1 and L2 frequency bands as listed in Table 2. Asthe TEC changes, so does the relative phase angle between the USB andLSB for both L1 and L2:θ_(relL1)(TECu)=TECu·3.9903075  (8)θ_(relL2)(TECu)=TECu·6.575261  (9)

-   -   where TECu is the total electron count unit 10¹⁶el/m².

For θ_(rel) to reach 360°, and thus, be indistinguishable from multiplecycle of the same phase, the TECu must increase by 54.8 TECu for the L2frequency band and 90.2 TECu for the L1 frequency band. Table 3 liststhe TEC range of M-Code frequencies and the TECu change to cause a 10°phase angle change. The TEC range for both L1 and L2 frequency band isless than 300 TECu range in the ionosphere 105 models. Therefore, someionosphere 105 assumptions such as the time of day and the angle ofelevation are used to measure the relative phase of the L2 or L1 bandand estimate the TEC value. For instance, the nominal TEC range for theL1 band is 90 TECu.

From Equation 6, the L1 band can calculate the TEC levels within a 12hour window (t=6 hours) provided that the Q factor does not exceed 1.8(φ˜27°).

Equation 6 also shows that if the TOD is known to within a 7.2 hr window(t=3.6 hrs), then no φ is required. When considering the L2 case, a 12hr window limits the Q to no greater than 1.08 (φ˜70°). In the L2 case,if Q=3 then a time window of 4.32 hours (t=2.16 hours) is required.Therefore, with a proper range of TOD and (φ it is possible to useeither the θ_(relL1) or θ_(relL2) to determine reasonable ionosphericcorrection errors.

TABLE 3 Signal Description TEC Range TECu/10° Relative L1 USB & LSB(θ_(relL1)) 90.2 TECu 2.51 Relative L2 USB & LSB (θ_(relL2)) 54.8 TECu1.52 Simultaneous Relative USB & LSB angles 1533.0 TECu  2.51(θ_(relL2), θ_(relL1))

While using the L1 band's θ_(rel) to make a TEC measurement is limitedby its TEC range, using the θ_(rel) for both L1 and L2 it is possible tomake a TEC measurement without making assumptions as to the time of dayand angle of elevation. Any naturally- occurring TEC values can beuniquely determined by implementing the θ_(rel) for both the L1 and L2frequency bands and comparing them with theoretical equations. Theθ_(rel) values as a function of TEC for both the L1 and L2 frequencybands from 0°-360° are shown in FIG. 4. The periodic behavior is easilyseen for both frequency bands. The L1 and L2 functions behave as shownin Equations 10 and 11, respectively. Since n and m are integers, it ispossible to write a software program to go through an iterative processof incrementing the n and m numbers until agreement between the twoequations is reached. This method recovers the lost cycle informationfor both bands.

$\begin{matrix}{{{{TECu}\left( \theta_{{relL}\; 1} \right)} = {\frac{\theta_{{relL}\; 1}}{3.9903075} + {n \cdot 90.218611}}}{where}\mspace{14mu}{n = {0,1,2,3,4\mspace{14mu}\ldots}}\mspace{11mu}{and}} & (10) \\{{{{TECu}\left( \theta_{{relL}\; 2} \right)} = {\frac{\theta_{{relL}\; 1}}{6.575211} + {m \cdot 54.750686}}}{where}{m = {0,1,2,3,4\mspace{14mu}\ldots}}} & (11)\end{matrix}$

With this information, the TEC value using θ_(rel) from the L1 and L2carrier frequencies can be calculated. The theoretical TECu value wherethe L1 θ_(rel) and L2 θ_(rel) are both near 0 occurs at 1533 TECu (n=17and m=28). This TECu value typically does not occur under naturalconditions. If the θ_(rel) can be determined within 1° then the TECrange is 1153 TECu, still well above any naturally occurring TEC level.A closer examination shows that at ˜270 TECu the L1 and L2 θ_(rel) canbe close enough to cause an incorrect TEC measurement. A TEC value of100 TECu in conjunction with a Q factor of 2.7 (φ=˜10°) registers a TECuvalue of 270 and so care is taken to deal with this relatively remotepossibility. A closer look at θ_(rel) error is useful for determininghow much error is allowed before a TEC measurement is unreliable. Whilethis technique does provide an ability to measure the ionosphere 105correction without any aids such as time of day and elevation angle, itdoes involve the use of two frequency bands. However, using twofrequency bands can improve the accuracy of the measurement, since theL1 and L2 phase measurements are relatively independent. Using twofrequency bands can also provide jamming resistance, since a jammerwould have to jam both bands to prevent ionospheric measurement.

Because of the dependence on the phase angle accuracy of the receiver102, the impact of jamming on such a measurement is considered. A reviewof common parameters reveals that the ability to track a signal suggeststhat a reasonable phase angle accuracy is approximately 15°. For arelatively static receiver 102, the jamming level should exceed a J/S of48 dB. The 15° phase error is used for evaluation of the relevantionosphere 105 correction methods.

One metric for performance is how much error, in terms of distance, iscreated due to the ambiguity of the relative phase angle measurementsfor the L1/L2 dual-band system as compared to the single-band USB andLSB method. The relative phase angle as a function of TEC and frequencyis given by Equation 12. Where θ_(ε) is the phase error in measuring theindividual carrier phases. The √{square root over (2)} factor isincluded because of the related error between measuring the carrierphase of both frequencies. Using Equation (12) and solving for TEC givesEquation (13).

$\begin{matrix}{{\Delta\;\theta_{ɛ}\sqrt{2}} = {\frac{{TEC} \cdot 360^{{^\circ}} \cdot 40.308}{c}\left( {\frac{1}{f_{2}} - \frac{1}{f_{1}}} \right)}} & (12) \\{{{{TEC} = \frac{\sqrt{2}\Delta\;{\theta_{ɛ} \cdot c}}{360^{{^\circ}} \cdot 40.308 \cdot \gamma}};}{where}{\gamma = \left( {\frac{1}{f_{2}} - \frac{1}{f_{1}}} \right)}} & (13)\end{matrix}$

Then using the TEC values the next step is to calculate the error timedelay (τ_(ε)) from Equation 12. The leads to the cancellation of someterms and yields the relation seen in Equation 14.

$\begin{matrix}{\tau_{ɛ} = \frac{\sqrt{2}\Delta\;\theta_{ɛ}}{360^{{^\circ}} \cdot \gamma \cdot f^{2}}} & (14)\end{matrix}$

To calculate the error in terms of distance, τ_(ε) is multiplied by c,the free space speed of propagation of the RF signal. The velocity tomultiply the τ_(ε) is the phase velocity of the wave. However, at theconsidered frequencies using c is accurate to at least three significantdigits. For a θ_(ε) of 15° the calculated range errors for the dualfrequency, L1 USB and LSB, L2 USB and LSB systems are listed in Table 4.The values in Table 4 indicate that the dual-band system is relativelyless sensitive to θ_(ε) than the single-band band system. The delayerror sensitivity for each system is a direct result of the differencebetween the two frequencies being used for the TEC calculation.

TABLE 4 Ionosphere 105 Spatial Delay Spatial Delay Spatial DelayCorrection Considered Error (m) for Error (m) for Error (m) for MethodFrequency θ_(ε) = 15° θ_(ε) = 1°$\theta_{ɛ} = \frac{360{^\circ}}{\sqrt{2}}$ Dual Frequency L1 0.033 m0.002 m 0.51 m Dual Frequency L2 0.060 m 0.004 m 1.02 m L1 USB & LSB L1USB 0.853 m 0.057 m 14.5 m L1 USB & LSB L1 LSB 0.874 m 0.058 m 14.8 m L2USB & LSB L2 USB 0.849 m 0.056 m 14.3 m L2 USB & LSB L2 LSB 0.877 m0.058 m 14.8 m

The delay error for the

$\frac{360^{{^\circ}}}{\sqrt{2}}$case shows that the spatial delay error is related to the wavelength ofthe frequency difference between the considered frequencies. Thedifference between the peaks of the GPS M code in the L1 frequency bandis 20.46 MHz which results in a wavelength of 14.6 m. The slightdifference between the USB and LSB in Table 4 is attributed to thespecific frequency being considered (USB or LSB). The difference betweenthe peaks of the L2 frequency band also results in a wavelength of ˜14.6m. Again the value in the last column is attributed to the specificfrequency being considered. The frequency difference between the L1 andL2 frequency is 347.82 MHz which results in a wavelength of ˜0.86 m.Here the discrepancy in the last column between the L1 and L2 frequencyis more pronounced because the two frequencies being considered differby a greater amount than the single-band method.

FIG. 6 is a block diagram of a receiver 600 that uses the USB and LSB ofa received signal to estimate one or more atmospheric parameters. In thereceiver 600, an antenna 601 receives a Radio-Frequency (RF) signal thathas propagated through a dispersive medium 610, such as, for example,the ionosphere. An RF signal from the antenna 601 is provided to an RFblock 602 that provides amplification and signal conditioning. Anamplified signal from the RF block 602 is provided to a downconverter603. The down converter downconverts the RF signal to baseband andprovides an LSB signal and a USB signal to an estimator 604. Theestimator 604 evaluates and compares the LSB and the USB and computesone or more estimates related to how propagation through the dispersivemedium affected the signal propagating through the dispersive medium610. In one embodiment, the estimator 604 estimates one or more physicalproperties of the dispersive medium 610. In one embodiment, theestimator 604 uses a phase difference between the USB and the LSB toestimate properties of the dispersive medium 610. In one embodiment, theestimator 604 produces an estimate of TEC. In one embodiment, thereceiver 600 is configured to compute ionospheric estimates for morethan one satellite and/or using LSB and USB phase measurements on one ormore frequency bands.

As described above, the ionosphere 105 is a dispersive (frequencydependent) media that affects the propagation path and velocity ofradio-frequency signals, including GPS signals. The relationship betweentime delay, frequency, and total electron count (TEC) is shown inEquation 15. The positive or negative value for t_(delay) corresponds towhether the signal being considered is a data signal (negative value,delayed), or a carrier wave (positive value, advanced). The TEC isdefined as the number of electrons present between the transmitter andreceiver 102 along a square meter column. The factors that influence theTEC are the amount of ionization in the atmosphere and the distancepropagated through the ionization (where the distance is related to theangle of elevation between the receiver 102 and the satellite 101).

$\begin{matrix}{t_{delay} = {\pm \frac{{TEC} \cdot 40.3}{{cf}^{2}}}} & (15)\end{matrix}$

The ionospheric distortion of GPS is a well documented effect ontraditional GPS signals. However, the implementation of the M Codesignal structure presents a new challenge for GPS receivers. The M-codesignal has two sidebands, the upper sideband (USB) centered at 1585.65MHz above the RF carrier, and the lower sideband (LSB) centered at1565.19 MHz below the RF carrier. The dispersive nature of theionosphere 105 introduces a phase difference between the LSB and theUSB.

For the M-code signals, the group delay between the LSB and USB is onlya few nanoseconds and is not measurably significant for realistic TECvalues. However, this delay can impact the carrier frequencies to thepoint where the time delays between the LSB and the USB are disruptiveto the combining of the sidebands for correlation and/or demodulationpurposes. A receiver with tracking channels for both USB and LSBcorrelators can provide carrier phase tracking between the LSB and theUSB of the L1 M-code signal and/or the L2 M-code signal.

To compensate for this effect, a carrier phase correction algorithm onthe downconverted baseband signal is applied to maximize the correlationvalues.

FIG. 7 is a block diagram of a GPS receiver 700 configured to providephase correction and estimation of ionospheric properties. In thereceiver 700, an antenna 701 provides an RF signal to an RF amplifiermodule 702. An output of the RF amplifier module 702 is provided to adownconverter 703. A downconverted signal from the downconverter 702 isprovided to a first input of a USB mixer 704, to a first input of an LSBmixer 714, and to an ionospheric estimator 730.

An output of the USB mixer 704 is provided to a USB lowpass filter 705.An output of the USB lowpass filter 705 is provided to a first input ofa USB correlator 706. An output of the USB correlators 706 is providedto a USB phase discriminator 707. An output of the USB phasediscriminator 707 is provided to a USB input of a phase correctionestimator 721.

An output of the LSB mixer 714 is provided to an LSB lowpass filter 715.An output of the LSB lowpass filter 715 is provided to a first input ofan LSB correlator 716. An output of the LSB correlators 716 is providedto an LSB phase discriminator 717. An output of the LSB phasediscriminator 717 is provided to an LSB input of the phase correctionestimator 721.

A phase correction output of the phase correction estimator is providedto a USB frequency shifter 708 and to an LSB frequency shifter 718. AUSB local oscillator (LO) output of the USB frequency shifter 708 isprovided to a second input of the USB mixer 704. An LSB LO output of theLSB frequency shifter 718 is provided to a second input of the LSB mixer714.

The ionospheric estimator 730 compares the phase of the USB with the LSBand uses the phase difference between the USB and the LSB to estimateone or more ionospheric parameters.

The phase and/or frequency of the LO signal from the USB frequencyshifter 708 are configured such that the USB mixer 704 in combinationwith the USB lowpass filter 705 operates as a phase-shifting demodulatorto extract the USB signal from the down-converted signal and to adjustthe phase of the USB signal to a desired value. Similarly, the phaseand/or frequency of the LO signal from the LSB frequency shifter 718 areconfigured such that the LSB mixer 714 in combination with the LSBlowpass filter 715 operates as a phase-shifting demodulator to extractthe LSB signal from the down-converted signal and to adjust the phase ofthe LSB signal to a desired value

The phase-adjusted USB signal from the USB lowpass filter 705 and thephase-adjusted LSB signal from the LDB lowpass filter 715 are providedto a combiner 724. An output of the combiner 724 is provided to a firstinput of a correlator 722. A reference code signal generator 720provides signal inputs to second inputs of the USB correlators 706, 716,and 722. An output of the correlator 722 comprises M-code data.

In the system 700, the baseband signal is split into upper and lowerpaths. The upper path is mixed with exp[−i2πf₀t+iθ₁] to center the USBat zero frequency. Then a digital low pass filter is used to remove theLSB sideband. The sideband code will then be correlated against thereceiver 102 replica code and the phase of the USB due to travelingthrough the ionosphere 105 will be measured. A similar process will beimplemented for the LSB using exp[+i2πf₀t+iθ₂]. The resulting phasesfrom the USB and LSB paths will be measured and inputted into the phasecorrection algorithm. It is paramount that the inverse tangent functionneeds to have a 4-quadrant capability and is computed from the evencorrelator outputs. The purpose of the phase correction algorithm is toread in the phases from USB and LSB and then output correction phases tothe USB path and LSB path so the phase difference between the twosidebands is zero. With the proper phase correction in place the USB andLSB sidebands can then be coherently combined and a 3 dB improvement incorrelation can then be realized.

In one embodiment, a programmable modulation sideband phase adjustmentis provided. This adjustment can be implemented during the phasecorrection process. Normally, the phase correction terms for USB and LSBare adjusted to ensure that the phase difference between the USB and LSBis small (e.g., substantially zero). However, any desired phasedifference between the USB and LSB sideband carrier frequency can beprovided. In one embodiment, the phase inputs are variable in time at arate of 1 Hz or more. In one embodiment, this phase adjustment isapplied to the modulation sidebands but not the code frequency.

In one embodiment, the receiver 700 with tracking channels for both USBand LSB correlators is used to provide carrier phase tracking betweenthe LSB 210 and the USB 202 of the L1 M-code signal and/or the L2 M-codesignal. This tracking channel can sequence through one or moresatellites 101 and provide ionospheric correction measurements, viacarrier phase corrections, for each satellite. The rate of change ofionospheric delay is such that the phase updates typically need notoccur more quickly than once every few seconds. This embodiment uses therelative phase angles (θ_(rel)) between the USB and the LSB of the L1and/or L2 frequency bands. Using relative carrier-phase measurementbetween the USB and the LSB for either the L1 of L2 frequency band, itis possible provide dual-frequency ionosphere data while maintaining thesimplicity of a single-band receiver.

The phase corrector 721 makes ionosphere 105 corrections of the USB andLSB signals. These corrections improve the correlation values for thecoherently combined USB and LSB sidebands. The phase corrector:

-   -   Measures the USB phase (θ₁) and the LSB phase (θ₂).    -   Determines the desired final phase θ_(f) for the USB and LSB        sidebands. Typically, θ_(f)=0.    -   Determines the phase corrections (θ_(1C), θ_(2C)) to insert so        that the final USB phase and final LSB phase are equal to θ_(f)        (Equations 16, 17).        θ_(1C)=θ_(1f)−θ₁  (16)        θ_(2C)=θ_(2f)−θ₂  (17)    -   Writes the phase values (θ_(1C), θ_(2C)) to the control        register.    -   Repeats the process at a desired update rate to maintain        coherent phase during ionospheric variations. In one embodiment,        the desired update rate is at least 1 Hz.

Although described in terms of specific embodiments, one of ordinaryskill in the art will recognize that other embodiments and variationsare within the scope of the invention. For example, the presentinvention is not limited to satellite systems or systems that propagatethrough the ionosphere, but, rather, can be used in connection with anysystem where waves propagate through a dispersive medium. The presentinvention is not limited to satellite navigation systems, but can beused in connection with other communication or navigation systems. Thesystem is not limited to GPS systems, but can be used with othernavigation systems, such as, for example, Galileo, GLONASS, etc. Thesystem is not limited to any particular modulation type and applies toany multicarrier modulation type including, but not limited to, offsetcarrier, binary offset carrier, Manchester encoded, orthogonal frequencydivision multiplexing, etc. Thus, the invention is limited only by theclaims.

1. A method of compensating for ionospheric delay, the methodcomprising: receiving a first modulated radio frequency signal from asatellite source; receiving a second modulated radio frequency signalfrom the satellite source; determining a first phase difference betweenan upper sideband and a lower sideband of the first modulated radiofrequency signal; determining a second phase difference between an uppersideband and a lower sideband of the second modulated radio frequencysignal; resolving integer phase ambiguity by using the first phasedifference and the second phase difference; and determining a correctionfor a range measurement to the satellite source based at least in parton the determined first phase difference and the determined second phasedifference.
 2. The method of claim 1, wherein the satellite source is aGlobal Positioning System (GPS) satellite, and wherein the firstmodulated radio frequency signal corresponds to L1 and the secondmodulated radio frequency signal corresponds to L2.
 3. The method ofclaim 2, wherein resolving integer phase ambiguity comprises determininginteger values for n and m such that the following are in agreement:${{{TECu}\left( \theta_{{relL}\; 1} \right)} = {\frac{\theta_{{relL}\; 1}}{3.9903075} + {n \cdot 90.218611}}};$and${{{TECu}\left( \theta_{{relL}\; 2} \right)} = {\frac{\theta_{{relL}\; 1}}{6.575211} + {m \cdot 54.750686}}};$wherein θ_(relL1) corresponds to the first phase difference, and whereinθ_(relL2) corresponds to the second phase difference.
 4. The method ofclaim 1, wherein determining the first phase difference comprises:tracking a first carrier phase corresponding to the upper sideband ofthe first modulated radio frequency carrier signal; tracking a secondcarrier phase corresponding to the lower sideband of the first modulatedradio frequency signal; and extracting a difference between said firstcarrier phase and said second carrier phase to determine the first phasedifference; and wherein determining the second phase differencecomprises: tracking a third carrier phase corresponding to the uppersideband of the second modulated radio frequency signal; tracking afourth carrier phase corresponding to the lower sideband of the secondmodulated radio frequency signal; and extracting a difference betweensaid third carrier phase and said fourth carrier phase to determine thesecond phase difference.
 5. An apparatus for compensating forionospheric delay, the apparatus comprising: a first receiver front endconfigured to receive a first modulated radio frequency signal from asatellite source; a second receiver front end configured to receive asecond modulated radio frequency signal from the satellite source; afirst phase discriminator configured to determine a first phasedifference between an upper sideband and a lower sideband of the firstmodulated radio frequency signal; a second phase discriminatorconfigured to determine a second phase difference between an uppersideband and a lower sideband of the second modulated radio frequencysignal; a resolver configured to resolve integer phase ambiguity byanalysis of the first phase difference and the second phase difference;and an estimator configured to determine a correction for a rangemeasurement to the satellite source based at least in part on thedetermined first phase difference and the determined second phasedifference.
 6. The apparatus of claim 5, wherein the satellite source isa Global Positioning System (GPS) satellite, and wherein the firstmodulated radio frequency signal corresponds to L1 and the secondmodulated radio frequency signal corresponds to L2.
 7. The apparatus ofclaim 5, wherein the resolver is further configured to determine integervalues for n and m such that the following are in agreement:${{{TECu}\left( \theta_{{relL}\; 1} \right)} = {\frac{\theta_{{relL}\; 1}}{3.9903075} + {n \cdot 90.218611}}};$and${{{TECu}\left( \theta_{{relL}\; 2} \right)} = {\frac{\theta_{{relL}\; 1}}{6.575211} + {m \cdot 54.750686}}};$wherein θ_(relL1) corresponds to the first phase difference, and whereinθ_(relL2) corresponds to the second phase difference.
 8. The apparatusof claim 5, wherein the first phase discriminator comprises: a firsttracker configured to track a first carrier phase corresponding to theupper sideband of the first modulated radio frequency signal; a secondtracker configured to track a second carrier phase corresponding to thelower sideband of the first modulated radio frequency signal; and afirst phase comparator configured to extract a difference between saidfirst carrier phase and said second carrier phase to determine the firstphase difference; and wherein the second phase discriminator comprises:a third tracker configured to track a third carrier phase correspondingto the upper sideband of the second modulated radio frequency signal; afourth tracker configured to track a fourth carrier phase correspondingto the lower sideband of the second modulated radio frequency signal;and a second phase comparator configured to extract a difference betweensaid third carrier phase and said fourth carrier phase to determine thesecond phase difference.